Question: Simplify the following expression: $x = \dfrac{a^2 + 2a - 15}{a - 3} $
Answer: First factor the polynomial in the numerator. $ a^2 + 2a - 15 = (a - 3)(a + 5) $ So we can rewrite the expression as: $x = \dfrac{(a - 3)(a + 5)}{a - 3} $ We can divide the numerator and denominator by $(a - 3)$ on condition that $a \neq 3$ Therefore $x = a + 5; a \neq 3$